scholarly journals Location and stability of the triangular Lagrange points in photo-gravitational elliptic restricted three body problem with the more massive primary as an oblate spheroid

2019 ◽  
Vol 7 (2) ◽  
pp. 57
Author(s):  
A. Arantza Jency ◽  
Ram Krishan Sharma
Keyword(s):  
Body Problem ◽  
Critical Mass ◽  
Oblate Spheroid ◽  
Motion Equation ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lagrangian Points ◽  
Mean Motion ◽  
The Mean ◽  
Three Body

The triangular Lagrangian points of the elliptic restricted three-body problem (ERTBP) with oblate and radiating more massive primary are studied. The mean motion equation used here is different from the ones employed in many studies on the perturbed ERTBP. The effect of oblateness on the mean motion equation varies. This change influences the location and stability of the triangular Lagrangian points. The points tend to shift in the y-direction. The influence of the oblateness on the critical mass ratio is also altered. But the eccentricity limit  for stability remains the same.   

scholarly journals Stationary solutions, critical mass, Tadpole orbits in the circular restricted three-body problem with the more massive primary as an oblate spheroid

2020 ◽  
Vol 13 (39) ◽  
pp. 4168-4188
Author(s):  
A Arantza Jency
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Critical Mass ◽  
Equations Of Motion ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Mean Motion ◽  
The Mean ◽  
Three Body

Background: The location and stability of the equilibrium points are studied for the Planar Circular Restricted Three-Body Problem where the more massive primary is an oblate spheroid. Methods: The mean motion of the equations of motion is formulated from the secular perturbations as derived by(1) and used in(2–4). The singularities of the equations of motion are found for locating the equilibrium points. Their stability is analysed using the linearized variational equations of motion at the equilibrium points. Findings: As the effect of oblateness in the mean motion expression increases, the location and stability of the equilibrium points are affected by the oblateness of the more massive primary. It is interesting to note that all the three collinear points move towards the more massive primary with oblateness. It is a new result. Among the shifts in the locations of the five equilibrium points, the y–location of the triangular equilibrium points relocate the most. It is very interesting to note that the eccentricities (e) of the orbits around L1 and L3 increase, while it decreases around L2 with the addition of oblateness with the new mean motion. The decrease in e is significant in Saturn-Mimas system from 0.95036 to 0.87558. Similarly, the value of the critical mass ratio mc, which sets the limit for the linear stability of the triangular points, further reduces significantly from 0:285: : :A1 to 0:365: : :A1 with the new mean motion. The mean motion sz in the z-direction increases significantly with the new mean motion from 9A1/4 to 9A1/2.

scholarly journals A general solution to non-collinear equilibria in terms of largest root (κ) of confocal oblate spheroid

2016 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
M Javed Idrisi
Keyword(s):  
General Solution ◽  
Body Problem ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Mean Motion ◽  
Three Body ◽  
Infinitesimal Mass

<p>This paper deals with the existence of non-collinear equilibria in restricted three-body problem when less massive primary is an oblate spheroid and the potential of oblate spheroid is in terms of largest root of confocal oblate spheroid. This is found that the non-collinear equilibria are the solution of the equations <em>r</em><sub>1</sub> = <em>n</em><sup>-2/3</sup> and κ = 1 – <em>a</em><sup>2</sup>, where <em>r</em><sub>1</sub> is the distance of the infinitesimal mass from more massive primary, <em>n</em> is mean-motion of primaries, <em>a</em> is semi axis of oblate spheroid and κ is the largest root of the equation of confocal oblate spheroid passes through the infinitesimal mass.</p>

scholarly journals Locations of Lagrangian points and periodic orbits around triangular points in the photo gravitational elliptic restricted three-body problem with oblateness

2019 ◽  
Vol 7 (2) ◽  
pp. 25
Author(s):  
Ancy Johnson ◽  
Ram Krishan Sharma
Keyword(s):  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Critical Mass ◽  
Stable Region ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lagrangian Points ◽  
Triangular Points ◽  
Three Body

Locations of the Lagrangian points are computed and periodic orbits are studied around the triangular points in the photogravitational elliptic restricted three-body problem (ER3BP) by considering the more massive primary as the source of radiation and smaller primary as an oblate spheroid. A new mean motion taken from Sharma et al. [13] is used to study the effect of radiation pressure and oblateness of the primaries. The critical mass parameter  that bifurcates periodic orbits from non-periodic orbits tends to reduce with radiation pressure and oblateness. The transition curves defining stable region of orbits are drawn for different values of radiation pressure and oblateness using the analytical method of Bennet [14]. Tadpole orbits with long- and short- periodic oscillations are obtained for Sun-Jupiter and Sun-Saturn systems.  

scholarly journals Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid

BIBECHANA ◽  
2014 ◽  
Vol 11 ◽  
pp. 149-156
Author(s):  
RR Thapa
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Independent Variable ◽  
The Stability ◽  
Three Body ◽  
Special Case

The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m1 = m2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m3 moves along the line perpendicular to plane of motion of primaries. Here oblate spheroid primaries are taken. The solution of the Sitnikov's circular restricted three body problem has been checked when the primaries are oblate spheroid. We observed that solution is depended on oblate parameter A of the primaries and independent variable τ = ηt. For this the stability of non-trivial solutions with the characteristic equation is studied. The general equation of motion of the infinitesimal mass under mutual gravitational field of two oblate primaries are seen at equilibrium points. Then the stability of infinitesimal third body m3 has been calculated. DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10395 BIBECHANA 11(1) (2014) 149-156

scholarly journals Solutions of the Sitnikov's circular restricted three body problems when primaries are oblate spheroid

BIBECHANA ◽  
2013 ◽  
Vol 10 ◽  
pp. 92-99
Author(s):  
RR Thapa ◽  
MR Hassan
Keyword(s):  
Body Problem ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

The solutions of sitnikov's circular restricted three body problem has been tried to obtain by using Lindstedt poincare method if the primaries are oblate spheroid. DOI: http://dx.doi.org/10.3126/bibechana.v10i0.9340   BIBECHANA 10 (2014) 92-99

scholarly journals Perturbation due to a Circumbinary Disc around L4,5 in the Photogravitational Elliptic Restricted Three-Body Problem

2021 ◽  
Vol 87 ◽  
pp. 22-36
Author(s):  
Umar Aishetu ◽  
Kamfa A. Salisu ◽  
Bashir Umar
Keyword(s):  
Gravitational Potential ◽  
Radiation Pressure ◽  
Body Problem ◽  
Mass Parameter ◽  
Critical Mass ◽  
Significant Shift ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Region Of Stability ◽  
Three Body

The motion is investigated of dust/gas particles in the elliptic restricted three-body problem (ER3BP) in which the less massive primary is an oblate spheroid and the more massive a luminous body surrounded by a circumbinary disk. The paper has investigated both analytically and numerically the effects of oblateness and radiation pressure of the primaries respectively together with the gravitational potential from a disk on the triangular equilibrium L4,5 of the system, all in the elliptic framework of the restricted problem of three bodies. The important result obtained therein is a move towards the line joining the primaries in the presence of any /all perturbation(s). A significant shift away from the origin as the radiation pressure factor decreases and oblateness of the smaller primary increase is also observed. It is also seen that, all aforementioned parameters in the region of stability have destabilizing tendencies resulting in a decrease in the size of the region of stability except the gravitational potential from the disc. The binary system Ruchbah in the constellation Cassiopeiae is an excellent model for the problem, using the analytic results obtained, the locations of the triangular points and the critical mass parameter are computed numerically.

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